Simplify $\frac{7}{\sqrt{14}-\sqrt{7}}$ by rationalising the denominator.

Step-by-step solution

1. Multiply numerator and denominator by the conjugate of the denominator: $\frac{7}{\sqrt{14}-\sqrt{7}}\cdot \frac{\sqrt{14}+\sqrt{7}}{\sqrt{14}+\sqrt{7}}$.
2. The numerator becomes $7(\sqrt{14}+\sqrt{7})$.
3. The denominator becomes $(\sqrt{14}{)}^2-(\sqrt{7}{)}^2=14-7=7$.
4. Cancel the common factor $7$: the expression simplifies to $\sqrt{14}+\sqrt{7}$.

Concept tested: Rationalising denominators

Published 16 October 2026 · How this solution was prepared and checked